The results of the combinations are given as follows:
A. Number of possible outcomes with red exactly 3 times and Purple exactly 2: 10.
B. Number of possible outcomes with red at least ounce in 4 spins: 175.
C. Number of possible outcomes with red at least ounce in 5 spins: 781.
How to obtain the number of outcomes?The outcomes are obtained in two ways, as follows:
Combination -> Item a, as it is an arrangement with repetition, which is equivalent to combination.Fundamental Counting Theorem -> Items b and c.CombinationThe combination formula calculates the number of different combinations of x objects from a set of n elements, according to the equation presented as follows:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
From item a, there are 5 outcomes with 3 and 2 repetitions, hence the number of results is obtained as follows:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
Fundamental Counting TheoremIt states that the number of outcomes of n independent trials is given by the multiplication of the number of outcomes for each trial.
For item b, we have that:
There are 4 spins.Each with 4 outcomes.Hence the total number of outcomes, without considering the restriction is:
Total = 4^4 = 256.
With no red results, the number of outcomes is:
Total no red = 3^4 = 81.
Hence the number of outcomes with at least one red result, considering complementary events, is:
256 - 81 = 175.
Item c follows the same logic, only with 5 trials instead of four, hence:
4^5 - 3^5 = 781.
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There are 4 times as many alligators as crocodiles. If the total number of alligators and crocodiles is 35 , how many alligators are there
Answer:
140
Step-by-step explanation:
It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.
Find the inverse of f(x) = 4x-1/-2x +2
The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:
y = (4x - 1)/(-2x +2)
x = (4y - 1)/(-2y +2)
Cross-multiplying, we have:
x(-2y +2) = 4y - 1
2x - 2xy = 4y - 1
Next, we would rearrange the function by collecting like terms as follows:
4y + 2xy = 2x + 1
y(4 + 2x) = 2x + 1
Dividing both sides of the function by (4 + 2x), we have:
y = (2x + 1)/(4 + 2x)
y = f⁻¹(x) = (2x + 1)/(4 + 2x)
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4 and 3 half's divided by 2 and 7
halfs minus 8
Answer:
4/3/2/7-8= -7
Step-by-step explanation:
6. Given AACP ALNX, find each missing measure. N 29° 13 cm P CX V L 21 cm a) XL = b) AC= c) PC = d) m/L= e) m/C= f) m/X=
The missing measure is ∠P =∠X = 122°
Given △ACP ≅ △LNX
XL = 13 cm, m∠L = 29°
AC = 21 cm, m∠C = 29°
PC = 13 cm, m∠Y = ?? (there is no angle Y)
On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.
PA = PC = XL = XN = 13 cm
In the same way, ...
LN = AC = 21 cm
Of course, the angles have a similar relationship:
∠A = ∠C = ∠L = ∠N = 29°
The two base angles in the triangle add to 58°, so the third angle is ...
180° -58° = 122°
∠P =∠X = 122°
As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.
Hence the answer is The missing measure is ∠P =∠X = 122°
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Use the discriminant to describe the roots of each equation. Then select the best description. 6x2 + 13x + 6 = 0
The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.
What is the nature of the roots of a quadratic equation?
In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:
D = b² - 4 · a · c
Where a, b, c are real coefficients of the quadratic equation.
There are three possibilities for the results of the discriminant:
D < 0, conjugated complex numbers.D = 0, equal real numbers.D > 0, different real numbers.First, write the quadratic equation:
6 · x² + 13 · x + 6 = 0
Second, collect the real coefficients of the polynomial:
(a, b, c) = (6, 13, 6)
Third, calculate the discriminant:
D = 13² - 4 · 6²
D = 169 - 144
D = 25
The quadratic equation has two roots that are real and different.
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Assume that x=2 and y =9 find values of the 2 Expressions 7x +4y and 4y + 7y
Answer: 50, 99
Step-by-step explanation:
we just have to substitute the values of x and y in the given expressions.
7(2)+4(9)=50
4(9)+7(9)=99
Answer:
Step-by-step explanation:
7x + 4y= 50 and 4y + 7y= 99
Since, x=2 and y=9
7x + 4y= 7*2 + 7*9= 14 + 36= 50
and similarly
4y + 7y= 4*9 + 7*9= 36 + 63= 99
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Please help. Find x and y. NEED ASAP
Answer:
x = 15 , y = 4
Step-by-step explanation:
If 3 or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally. then
[tex]\frac{x}{5}[/tex] = [tex]\frac{18}{6}[/tex] = 3 ( multiply both sides by 5 )
x = 15
and
[tex]\frac{12}{y}[/tex] = 3 ( multiply both sides by y )
12 = 3y ( divide both sides by 3 )
4 = y
Savannah is flying a kite, holding her hands a distance of 2.5 feet above the ground
and letting all the kite's string play out. She measures the angle of elevation from her
hand to the kite to be 32. If the string from the kite to her hand is 75 feet long, how
many feet is the kite above the ground? Round your answer to the nearest tenth of a
foot if necessary.
Answer:
feet Submit Prowes
Z
Answer:
42.2 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.
We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Substituting θ = 32° and H = 75 into the ratio, we get:
[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]
[tex]\textsf{O}=75\sin 32^{\circ}[/tex]
[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.
In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.
[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]
Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).
Just please help im desperate( 3 different questions)
Answer:
7. what are the fold down options for this question exactly?
1. C and E
3. B and D
Step-by-step explanation:
7.
1. function 1 has a slope of 2/3 and function 2 has a slope of 3 so they are both positive rates of change, and the y intercept (the value that y has when it passes through x = 0) for function 1 is -6 while the y intercept for function 2 is -3.
3. K has a y intercept of 8 compared to the 3 that J has, and J has a slope of 5 compared to the 3 that K has.
The UK currently has a progressive income tax system. The rules are as follows: Any earnings under 11,500 GBP are taxed at 0%. Any earnings between 11,500 GBP and 33,500 GBP are taxed at 20%. Any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%. Any earnings above 150,000 GBP are taxed at 50%. A person earns 50,000 GBP gross. How much tax do they pay? Round your answer to the nearest GBP.
The amount of tax that the executive would pay on his income is; 20000 GBP
How to calculate tax deductions?Tax is defined as a compulsory payment that is levied on the income or on the sales of specific goods and services. Tax is usually imposed by the government to get a variety of macroeconomic objectives.
Now, income tax is the tax that is levied on the income of an individual. There are different types of taxes, such as progressive tax which levies a higher tax percentage on those that earn higher incomes This means invariably that the tax rate increases as income increases.
We are given;
Gross Amount executive earns = 50,000 GBP.
We are told that any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%.
Thus;
Tax that would be paid = tax rate * gross income
Tax that would be paid = 50000 * 0.4 = 20000 GBP
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Answer: 11,000
Step-by-step explanation:
The person earns 50,000 GBP, so they will stop at the tier 3 level of tax.
The first 11,500 GBP is tax free. They will be taxed 20% on (33,500−11,500)=22,000 GBP, and they will be taxed 40% on (50,000−33,500)=16,500 GBP. Hence the total tax (in GBP) they need to pay is
Total Income Tax=11,500×0%+22,000×20%+16,500×40%=0+22,000×20100+16,500×40100=0+4,400+6,600=11,000
Can you please assist me
5.1 The amount of money received by the man at the end of 4 years is
$10,217.39
5.2 The rate of interest per annum is 94.56%/year.
Given:
P=5000
r = 18%
t= 4 years.
5.1 First, convert R as a percent to r as a decimal
r = R/100
r = 18/100
r = 0.18 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 5,000.00(1 + 0.18/12)(12)(4)
A = 5,000.00(1 + 0.015)(48)
A = $10,217.39
5.2 Given:
P = 3700
A = 8360,34
t = 7 years.
r =?
Solving for rate r as a decimal
r = n[(A/P)1/nt - 1]
r = 2 × [(836,034.00/3,700.00)1/(2)(7) - 1]
r = 0.945604
Then convert r to R as a percentage
R = r * 100
R = 0.945604 * 100
R = 94.56%/year
Hence we get the required answer.
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Can you calculate the area of this land and if so, can you help me?
Se podría calcular el area de este terreno? y si es así pueden ayudarme?
The area of the rectangular land is 208,607 square meters,
A rectangle is defined as a quadrilateral whose opposite sides are equal and parallel
How to find the area of a rectangle?
The lengths of a rectangle are denoted by L and W
where: L=length
w=width
Area of the land (A)= Area of the larger land minus Area of the smaller land carved out
A= (LW) - (lw)
A=(513x466.5)-(267x113)
A=239,312-30705
A=208.607 meters square
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Write a linear equation that passes through
the points (-3, 3) and (9, -13).
In Point - Slope form.
The point slope form of equation is y- 3 = -4/3( x- (-3)).
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Points= (-3, 3) and (9, -13)
Now,
slope= (-13 - 3)/ (9 - (-3))
slope= -16 / 12
slope= -4/3
Now, the point slope form
y- [tex]y_1[/tex] = m (x- [tex]x_1[/tex])
y- 3 = -4/3( x- (-3))
y- 3= -4/3x - 4
y= -4/3x - 1
Hence, the point slope for of equation is y- 3 = -4/3( x- (-3)).
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Will give Brainliest if you can answer thesw questions
Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.
What is information?Information is defined as the content of a message which is passed from a source to its receiver.
The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2
The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.
To calculate for one hour for both would be addition of the derived fractions;
= 1/2 + 1/3
= 3+2/6
= 5/6
When converter to minutes, multiple by 60;
= 5/6 × 60
= 300/6
= 50 minutes.
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A friend has a 85% average before the final for a course. That score includes everything but the final, which counts for 20% of the course grade. a.) What is the best course grade your friend can earn? % b.) What is the minimum score your friend would need on the final to earn a 75% for the course? % Give answers accurate to at least one decimal place.
The best course grade your friend can earn is 88%.
The minimum score your friend needs to have on the final to earn a 75% for the course is 35%.
What is the minimum score your friends needs to have on the final exam?If the final counts for 20% of the course grade, it means that the average of 85% counts for 80% (100 - 20%) of the total score.
The linear expression that can be used to determine the best course grade your friend can earn is:
(average that has already been accumulated x 80%) + (score on the finals x 20%)
(85% x 80%) + (20% x 100%)
(85% x 0.80) + (0.2 x 100%)
68 + 20 = 88%
The linear equation that can be used to determine the minimum score that can be earned on the final to have75% in the course is
Final grade = (total average before the final x 80%) + (score on the final x 20%)
75% = (85% x 80%) + (f x 20%)
75% = (85% x 0.80) + (0.20 x f)
75% = 68% + 0.20f
75% - 68% = 0.20f
7 = 0.20f
f = 7% / 0.20
f = 35%
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(7x² + 4y²)(5x² - y²)
Answer:
okay so step by step explanation,
first multiply 7[tex]x^{2}[/tex] with 5[tex]x^{2}[/tex] and -[tex]y^{2}[/tex]
35[tex]x^{4}[/tex]-7[tex]x^{2}[/tex][tex]y^{2}[/tex]
then do the second one
20[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]
take the sum of those,
35[tex]x^{4}[/tex]+13[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]
good luck<3!
Tristan, Kimberly, and Dominic had a challenge to see who could run the
most in one day. Tristan ran 7 miles. Kimberly ran 4 times as many miles as
Tristan, and Dominic ran 2 times as many miles as Kimberly. How many
miles did Dominic run?
Answer: 56 miles
Step-by-step explanation:
Tristan ran 7 miles, multiply by 4 because Kimberly ran 4 times as many miles as Tristan. 7x4=28
Next, 28x2=56 because Dominic ran 2 times as many miles as Kimberly, which is 28 times 2.
So Dominic ran 56 miles in total.
please help me I don't understand pleaseeeee I'm begging youuuuu
The equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0 and the slope of the line is 1/8
Slope of the line that passes through the points (9,9) and (1, 8)
The equation of the line is
y -y₁ = ((y₂ - y₁)/ (x₂ - x₁)) (x - x₁)
y - 9 = ((8 - 9)/(1 - 9)) (x - 9)
y - 9 = (1/8) (x - 9)
8y - 72 = x - 9
8y - x - 63 = 0
8y = 1/8 (x + 63)
Therefpre, the equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0
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b) The diagram shows a thin square sheet of metal measuring 24 cm by 24 cm. A square of side x cm is cut off from each corner. The remainder is then folded to form an open box, x cm deep, whose square base is shown shaded in the diagram. Write the volume, cm³, of the box as V=4x³-96x² +576x [3]
(ii) Compute the maximum cost paid to fill up the box with sand if RM 0.30 per cubic centimeter of sand charged. [2]
Answer:
Below
Step-by-step explanation:
Graphing the equation shows local max volume at x = 4 of 1024 cm^3
1024 cm^3 * RM . 30 / cm^3 = RM 307.2
Identify each number between 2.6×10^-1 and 29.5%. Select all that apply. Responses 2.7×10^1
0.2875
2/7
2.8%
Numbers between 2.6×10^-1 and 29.5% are
0.28752/7How to write the numbers to decimal2.6 × 10^-1 in exponential form written in decimal as 0.26
29.5% in percentage written in decimal as 0.295
2/7 in fraction written in decimal as 0.2857
2.8% in percentage written in decimal as 0.028
0.2875 already in decimal form
the problem asks of numbers from 0.26 to 0.295
comparing the numbers shows that the numbers in this range are
0.2875 and 2/7
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use the formula for the area of the circle and the dimensions you listed in level 5 to explain the formula for the area of a circle (r2).
The formula for the area of a circle is given as follows:
A = πr².
How to obtain the area of a circle?The area of a circle of radius r is given by the multiplication of the number π and the square of the radius, according to the equation presented as follows:
A = πr².
Hence, for example, for a circle of radius of 5 units, the area is given as follows:
A = π x (5 units)² = 25π units².
The diameter of a circle is twice the radius, hence the radius is half the diameter, and as a function of the diameter, the area will be given as follows:
A = 0.25πd².
As the diameter in the context of this problem is:
r² = (0.5d)² = 0.25d².
Missing InformationThe problem is incomplete, hence the area of the circle was explained in general terms.
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Which of the following is an example of a conditional statement?
Calculate the rate of change of function f(x)= sqaure root of x - 1/square root of x
The rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.
We know that the rate of change of a function is nothing but the slope of the line.
The slope of the line is given by;
Slope = Change in y-coordinate / change in x-coordinate
We are given;
[tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex]
We need to find the rate of change of function for x = 4 and x = 9.
Let us find the value of y or f(x) for the given value of x.
For x = 4, [tex]f(x) = \sqrt{4} - \frac{1}{\sqrt{4}}[/tex] = 2 - 1/2 = 4 - 1 / 2 = 3 / 2
For x = 9, [tex]f(x) = \sqrt{9} - \frac{1}{\sqrt{9}}[/tex] = 3 - 1/3 = 9 - 1 / 3 = 8 / 3
Put the values of x and y in the slope formula, we will get;
Slope = (8 / 3 - 3 / 2) / (9 - 4) = 7 / 6*5 = 7 / 30
So, the rate of change of function is 7 / 30.
Thus, the rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.
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At the end of year 5, the account was valued at $3203.19. At the end of year 6, the account was valued at $3315.30. What was the interest rate, as a percent?
well, from the end of year 5 to the end of year 6 is only 1 year later, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]
Find the square root of:
441
It is very easy, we just have to take the square root as it tells us in the problem:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]
You may ask ¿why 21?
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \longmapsto \orange{21} [/tex]
Suppose the number cube was rolled 500 times. Based on the results in the table, about how many times would it land on 5?
The number of times that the cube will land on 5 if the number cube was rolled 500 times is 83 times.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
It should be noted that in a number cube, we hage numbers from 1 to 6. The probability of getting a 5 is 1/6.
Therefore, when it's rolled 500 times, the possible number will be:
= 1/6 × 500
= 83 times.
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617/50 into simplest form
Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.
617/50
600/50 = 12
617/50 = 12 17/50
On a farm the ratio of grey goats to white is 4:7 there are 160 grey goats. How many white goats are there
Answer: 88
Step-by-step explanation:
For every 7 grey goats there are 4 white goats. 160/7=22 4*22=88
Valerie is 64 inches tall. About how many centimeters tall is Valerie?
(1 inch -2.5 centimeters)
O 25.5
O 30.6
O 160
O 180
Using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.
What is the conversion factor?A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.
The amount is often expressed as a fraction or ratio with a multiplication factor.
For instance, 12 inches equals one foot when converting between inches and feet.
So, 64 inches in cm is:
We know that:
1 inch = 2.5 cm
Then, 64 inches is:
64 inches = 2.5 × 64
64 inches = 160
Therefore, using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.
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Correct question:
Valerie is 64 inches tall. About how many centimeters tall is Valerie?
(1 inch -2.5 centimeters)
A. 25.5
B. 30.6
C. 160
D. 180
A coach has to form 4 doubles teams from 8 badminton players. In how many ways can he form the teams? (A doubles team is a pair of players, and a player cannot be a member of more than one doubles team.)
The number of ways he can form the teams would be = 336 ways.
What is badminton?Badminton is a type of racket game that makes use of single or double players where by they make use of a racket to hit a shuttlecock over the net to their opponents side.
The number of players available for the badminton game = 8
The number of teams to the formed = 4
To find the number of ways to form 4 double teams from these 8 players would be to find the factorials of 8 divided by factorial 4.
That is ;
8!/4! = 8×7×6×4×3×2×1/4×3×2×1
= 8064/ 24
= 336 ways.
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